X3671

X958com(INTOUCH TRIANGLE)

Let O* be a circle with center X2 and variable radius R*. Let LA be the radical axis of O* and the A-excircle, and define LB and LC cyclically. Let A'=LB∩LC, and define B' and C' cyclically. There is a unique value of R* for which triangle A'B'C' is perspective to ABC, and the perspector is X3671. (Randy Hutson, January 15, 2019)
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) incircle: Incircle of △ABC { 1, 7 }: Soddy Line { 10, 12 }: Central Line L(10, 12) { 56, 551 }: Central Line L(56, 551) { 388, 519 }: Central Line L(388, 519) { 142, 960 }: Central Line L(142, 960) { 57, 1125 }: Central Line L(57, 1125) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_7 = GERGONNE POINT (0.5903, 0.2769) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_551 = MIDPOINT OF X(1) AND X(2) (0.5544, 0.2166) X_388 = ∩X(7)X(8) (0.5790, 0.2635) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_960 = INTERSECTION OF LINES X(1)X(6) AND X(5)X(10) (0.5041, 0.1533) X_57 = ISOGONAL CONJUGATE OF X(9) (0.6138, 0.3110) X_1125 = COMPLEMENT OF X(10) (0.5459, 0.2083) X_3671 = com(INTOUCH TRIANGLE) (0.5885, 0.2728) A B C X1 X7 X10 X12 X56 X551 X388 X519 X142 X960 X57 X1125 X3671 (a, b, c) = (5, 6, 7) | AB = 1

X3671 (X958com(INTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \((b + c)(3a + b + c)/(b + c - a) : :\)
Search Value (6, 9, 13): \(0.792557272124\)
▸ Incident Central Lines20 lines

{1, 7}, {2, 3339}, {10, 12}, {40, 3487}, {56, 551}, {57, 1125}, {142, 960}, {355, 1159}, {388, 519}, {496, 942}, {527, 958}, {938, 1699}, {950, 1836}, {1400, 3294}, {1697, 3475}, {1727, 3338}, {2093, 3085}, {2099, 3244}, {3361, 3616}, {3474, 3601}

▸ Functional Relations2 relations